Eddie Nketiah, signed on loan from Arsenal last week, opened the scoring on debut just before the interval after Salford created the better of the early chances.
Further goals from Gaetano Berardi and Mateusz Klich secured victory for Marcelo Bielsa’s side.
Despite the result, it was a good occasion for the fast-emerging Salford. As has been their case throughout their rapid rise through the football pyramid, there were plenty of eyes on them.
Being part-owned by the famous ‘Class of 92’ brings attention and, to add to that, this time Sir Alex Ferguson and Denis Law were among those watching. The players also had to play knowing one of the co-owners, Gary Neville, would be analysing their performances in his role as a TV pundit.
But if that and coming up against top-rated Championship opposition brought extra pressure, Salford did not show it early on.
Oscar Threlkeld shot straight at Kiko Casilla from the edge of the area and a powerful volley by Richie Towell was headed clear by Leeds winger Jack Clarke.
Salford went close again when Emmanuel Dieseruvwe flicked on to release Towell and his cross found Jake Beesley but Casilla was equal to the shot that followed. Dieseruvwe also headed over from an Ibou Touray cross.
Leeds began to take charge in the latter stages of the first half with Ezgjan Alioski lively on the left.
Kalvin Phillips tested Neal with a firm shot and the Salford keeper also had to deal with a deflected Clarke effort.
Pressure finally paid off when Jamie Shackleton found Helder Costa on the right and his low ball was turned in at close range by Nketiah.
Salford responded well to the setback and Danny Whitehead had an effort deflected wide on the stroke of half-time.
Leeds doubled their lead soon after the restart when Costa swung in a corner to the near post and Berardi brilliantly flicked in.
Again Salford looked to hit back as Dieseruvwe and Danny Whitehead shot at Casilla but Leeds put the game beyond doubt just before the hour.
The visitors broke quickly after clearing a Salford corner and Klich powered towards the area before curling a fine effort beyond Neal, with aid of a slight deflection.
That ended Salford’s hopes but they fought on and Nathan Pond went close before Adam Rooney headed narrowly wide after Casilla had saved from Towell.
Salford City: Neal, Joey Jones, Pond, Piergianni, Maynard, Threlkeld (Gaffney 62), Towell, Whitehead, Touray, Beesley (Lloyd 69), Dieseruvwe (Rooney 70). Unused substitutes: Wiseman, Letheren, Dan Jones, Smith.
Leeds: Casilla, Berardi, White, Davis, Alioski (Harrison 78), Phillips, Helder Costa, Shackleton, Klich, Clarke (McCalmont 70), Nketiah (Bamford 78). Unused substitutes: Dallas, Miazek, Bogusz, Gotts.
Referee: K Stroud (Hampshire).